LONDON (Reuters) - Prime Minister David Cameron will promise on Thursday to do whatever is needed to protect Britain's economy and banks from a break-up of the euro zone, and will urge leaders of the single currency bloc to "sort out its problems".

Cameron's remarks, in a speech to business leaders in northwest England, are likely to irritate European leaders trying to keep the euro zone intact as Greece prepares for a new election and struggles to cope with its debt crisis.

Britain's Conservative-led coalition has long blamed its own economic woes on the turbulence in Europe, its main trading partner, though critics say Cameron's tough austerity measures have also helped push Britain back into recession this year.

Cameron, under pressure to appease the unruly anti-European Union wing of his Conservative party, blocked an EU economic pact last year that was supposed to help shore up the euro zone. Seventeen of the 27 EU members - but not Britain - use the euro currency.

"Either Europe has a committed, stable, successful euro zone with an effective firewall, well capitalised and regulated banks, a system of fiscal burden sharing, and supportive monetary policy - or we are in uncharted territory which carries huge risks for everybody," Cameron will say, according to extracts from his speech released in advance.

"As I have consistently said, it is in Britain's interest for the euro zone to sort out its problems. But be in no doubt: whichever path is chosen, I am prepared to do whatever is necessary to protect this country and secure our economy and financial system."

The Bank of England said on Wednesday it had been planning for the possibility of a euro zone break-up for some time, with a focus on what banks should do to protect themselves.

Cameron and his finance minister George Osborne, who is slashing government spending as part of a seven-year austerity plan, have made a point of lecturing their European neighbours on the need to get their public finances in order.

A return to recession in Britain has led to demands for Osborne to soften his austerity plan, but the government has said that financial markets would not tolerate any deviation from the course they have set.

"We must resist dangerous voices calling on us to retreat," Cameron will say.